Closing a STL surface
Update 19/01/2021 (Solution)
I finally found a way to this by using the knife tool. After searching I found this video which had exactly what I needed. The info from @Gorgious and @Carlo in the comments helped me get a better direction. In short the process is the following:

Use the knife tool
Create a cut, just above the end, to have different surfaces
Following the instructions of the video, to rip the selection and then separate the meshes, delete the small object at the base of the head.